1,721,064 research outputs found
RESONANT ACTIVATION OF A BROWNIAN PARTICLE OUT OF A POTENTIAL WELL - REMARKS ON SOME RECENT THEORETICAL AND EXPERIMENTAL INVESTIGATIONS
No full textUNITARY POINT-OF-VIEW ON THE PUZZLING PROBLEM OF NONLINEAR-SYSTEMS DRIVEN BY COLORED NOISE
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STATE DEPENDENT FLUCTUATIONS - A CASE-STUDY WITH PROPERTIES BOTH OF INTERNAL AND EXTERNAL KIND
No full textScaling detection in time series: Diffusion entropy analysis
Full text linkThe methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where ordinary statistical properties hold true even if strange kinetics are involved. We illustrate a method of statistical analysis based on the Shannon entropy of the diffusion process generated by the time series, called diffusion entropy analysis (DEA). We adopt artificial Gauss and Lévy time series, as prototypes of ordinary and anomalous statistics, respectively, and we analyze them with the DEA and four ordinary methods of analysis, some of which are very popular. We show that the DEA determines the correct scaling exponent even when the statistical properties, as well as the dynamic properties, are anomalous. The other four methods produce correct results in the Gauss case but fail to detect the correct scaling in the case of Lévy statistics
KRAMERS PROBLEM FOR OVERDAMPED SYSTEMS DRIVEN BY CORRELATED NOISE - RESULTS FOR VANISHING DIFFUSION-COEFFICIENTS
No full textSporadic randomness: The transition from the stationary to the nonstationary condition
No full textWe address the study of sporadic randomness by means of the Manneville map. We point out that the Manneville map is the generator of fluctuations yielding the Levy processes, and that these processes are currently regarded by some authors as statistical manifestations of a nonextensive form of thermodynamics. For this reason we study the sensitivity to initial conditions with the help of a nonextensive form of the Lyapunov coefficient. The purpose of this research is twofold. The former is to assess whether a finite diffusion coefficient might emerge from the nonextensive approach. This property, at first sight, seems to be plausible in the nonstationary case, where conventional Kolmogorov-Sinai analysis predicts a vanishing Lyapunov coefficient. The latter purpose is to confirm or reject conjectures about the nonextensive nature of Levy processes. We find that the adoption of a nonextensive approach does not serve any predictive purpose: It does not even signal a transition from a stationary to a nonstationary regime. These conclusions are reached by means of both numerical and analytical calculations that shed light on why the Levy processes do not imply any need to depart from the adoption of traditional complexity measures
Levy scaling: The diffusion entropy analysis applied to DNA sequences
No full textWe address the problem of the statistical analysis of a time series generated by complex dynamics with the diffusion entropy analysis (DEA) [N. Scafetta, P. Hamilton, and P. Grigolini, Fractals 9, 193 (2001)]. This method is based on the evaluation of the Shannon entropy of the diffusion process generated by the time series imagined as a physical source of fluctuations, rather than on the measurement of the variance of this diffusion process, as done with the traditional methods. We compare the DEA to the traditional methods of scaling detection and prove that the DEA is the only method that always yields the correct scaling value, if the scaling condition applies. Furthermore, DEA detects the real scaling of a time series without requiring any form of detrending. We show that the joint use of DEA and variance method allows to assess whether a time series is characterized by Lévy or Gauss statistics. We apply the DEA to the study of DNA sequences and prove that their large-time scales are characterized by Lévy statistics, regardless of whether they are coding or noncoding sequences. We show that the DEA is a reliable technique and, at the same time, we use it to confirm the validity of the dynamic approach to the DNA sequences, proposed in earlier work
Levy statistics in coding and non-coding nucleotide sequences
No full textThe diffusion entropy analysis measures the scaling of the probability density function (pdf) of the diffusion process generated by time series imagined as a physical source of fluctuations. The pdf scaling exponent, delta, departs in the non-Gaussian case from the scaling exponent HV evaluated by variance based methods. When delta=1/(3-2H) Lévy statistics characterizes the time series. With the help of artificial sequences that are proved to be statistically equivalent to the real DNA sequences we find that long-range correlations generating Lévy statistics are present in both coding and non-coding DNA sequences
MULTIPLICATIVE STOCHASTIC-PROCESSES IN NONLINEAR-SYSTEMS .2. CANONICAL AND NONCANONICAL EFFECTS
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